{
 "cells": [
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   "cell_type": "markdown",
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   "source": [
    "# The Laplace Transform\n",
    "\n",
    "*This Jupyter notebook is part of a [collection of notebooks](../index.ipynb) in the bachelors module Signals and Systems, Communications Engineering, Universität Rostock. Please direct questions and suggestions to [Sascha.Spors@uni-rostock.de](mailto:Sascha.Spors@uni-rostock.de).*"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Definition\n",
    "\n",
    "The [Laplace transform](https://en.wikipedia.org/wiki/Laplace_transform) constitutes an integral transform with the complex exponential function $e^{s t}$ as kernel. It maps a complex-valued signal $x(t) \\in \\mathbb{C}$ with real-valued independent variable $t \\in \\mathbb{R}$ into its complex-valued Laplace transform $X(s) \\in \\mathbb{C}$ with complex-valued independent variable $s \\in \\mathbb{C}$. The Laplace transform is named after its discoverer [Pierre-Simon Laplace](https://en.wikipedia.org/wiki/Pierre-Simon_Laplace).\n",
    "\n",
    "Complex exponential functions constitute eigenfunctions of linear time-invariant (LTI) systems. The Laplace transform is therefore of special use in the context of signals and LTI systems. It is introduced in the following."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Two-Sided Laplace Transform\n",
    "\n",
    "The two-sided (or bilateral) Laplace transform is defined as\n",
    "\n",
    "\\begin{equation}\n",
    "X(s) = \\int_{-\\infty}^{\\infty} x(t) \\, e^{- s t} \\; dt\n",
    "\\end{equation}\n",
    "\n",
    "where $X(s) = \\mathcal{L} \\{ x(t) \\}$ denotes the Laplace transform of $x(t)$. A complex signal $x(t) \\in \\mathbb{C}$ with real-valued independent variable $t \\in \\mathbb{R}$ is represented by its complex valued Laplace transform $X(s) \\in \\mathbb{C}$ with complex independent variable $s \\in \\mathbb{C}$. The variable $s$ can be interpreted as [complex frequency](../continuous_signals/standard_signals.ipynb#Complex-Exponential-Signal) $s = \\sigma + j \\omega$ with $\\sigma, \\omega \\in \\mathbb{R}$.\n",
    "\n",
    "Whether a Laplace transform $X(s) = \\mathcal{L} \\{ x(t) \\}$ exists depends on the complex frequency $s$ and the signal $x(t)$ itself. All values $s$ for which the Laplace transform converges form a [*region of convergence*](https://en.wikipedia.org/wiki/Radius_of_convergence) (ROC). The Laplace transforms of two different signals may differ only with respect to their ROCs. Consequently, the ROC needs to be explicitly given for an unique inversion of the Laplace transform."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### One-Sided Laplace Transform\n",
    "\n",
    "Causal signals play an important role in the theory of signals and system. For a causal signal $x(t) = 0$ for $t <0$, the relation $x(t) = x(t) \\cdot \\epsilon(t)$ holds. Introducing this into the definition of the two-sided Laplace transformation yields\n",
    "\n",
    "\\begin{equation}\n",
    "X(s) = \\int_{-\\infty}^{\\infty} x(t) \\cdot \\epsilon(t) \\, e^{- s t} \\; dt = \\int_{0}^{\\infty} x(t) \\, e^{- s t} \\; dt\n",
    "\\end{equation}\n",
    "\n",
    "This motivates the definition of a one-sided Laplace transform\n",
    "\n",
    "\\begin{equation}\n",
    "X(s) = \\int_{0}^{\\infty} x(t) \\, e^{- s t} \\; dt\n",
    "\\end{equation}\n",
    "\n",
    "In the literature both the one- and two-sided Laplace transform are termed as Laplace transform. Both give the same result for causal signals."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Transformation of the Dirac Impulse\n",
    "\n",
    "The transform $\\mathcal{L} \\{ \\delta(t) \\}$ of the [Dirac impulse](../continuous_signals/standard_signals.ipynb#Dirac-Impulse) is derived by introducing $\\delta(t)$ into the definition of the two-sided Laplace transform and exploiting the sifting property of the Dirac delta function\n",
    "\n",
    "\\begin{equation}\n",
    "\\mathcal{L} \\{ \\delta(t) \\} = \\int_{-\\infty}^{\\infty} \\delta(t) \\, e^{- s t} dt = e^{- s t} \\Big\\vert_{t=0}  =  1\n",
    "\\end{equation}\n",
    "for $s \\in \\mathbb{C}$. The ROC covers the entire complex plane.\n",
    "\n",
    "The transform of the Dirac impulse is equal to one. Hence, all complex frequencies $s$ are present with equal weight. This is an important property in the theory of signals and systems, since the Dirac impulse is used to characterize linear time-invariant (LTI) systems by their [impulse response](../systems_time_domain/impulse_response.ipynb) $h(t) = \\mathcal{H} \\{ \\delta(t) \\}$."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Example - Transformation of the Dirac impulse**\n",
    "\n",
    "The Laplace transform of the Dirac impulse can be derived in `SymPy` by direct evaluation of above integral"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [
    {
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      "text/latex": [
       "$$1$$"
      ],
      "text/plain": [
       "1"
      ]
     },
     "execution_count": 1,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "%matplotlib inline\n",
    "import sympy as sym\n",
    "sym.init_printing()\n",
    "\n",
    "t = sym.symbols('t', real=True)\n",
    "s = sym.symbols('s', complex=True)\n",
    "\n",
    "X = sym.integrate(sym.DiracDelta(t)*sym.exp(-s*t), (t, -sym.oo, sym.oo))\n",
    "X"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Exercise**\n",
    "\n",
    "* Derive the two-sided Laplace transform of a shifted Dirac impulse $\\delta(t - \\tau)$ either by manual evaluation of the integral or by modification of above example.\n",
    "\n",
    "* Derive the one-sided Laplace transform of a shifted Dirac impulse $\\delta(t - \\tau)$. Hint: Differentiate between the cases $\\tau < 0$ and $\\tau > 0$."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Transformation of the Causal Complex Exponential Signal\n",
    "\n",
    "The transform $X(s) = \\mathcal{L} \\{ x(t) \\}$ of the causal complex exponential signal\n",
    "\n",
    "\\begin{equation}\n",
    "x(t) = \\epsilon(t) \\cdot e^{-s_0 t}\n",
    "\\end{equation}\n",
    "\n",
    "with complex frequency $s_0 \\in \\mathbb{C}$ is derived by evaluation of the definition of the one-sided Laplace transform\n",
    "\n",
    "\\begin{equation}\n",
    "\\begin{split}\n",
    "X(s) &= \\int_{0}^{\\infty} e^{-s_0 t} \\cdot e^{-s t} \\; dt = \\frac{-e^{-(s+s_0)t}}{s+s_0} \\, \\bigg\\vert_{0}^{\\infty} = \\frac{-1}{s+s_0} \\left[ \\lim_{t \\to \\infty} \\left( e^{- (s+s_0) t} \\right) -1 \\right] \\\\\n",
    "&= \\frac{1}{s + s_0}\n",
    "\\end{split}\n",
    "\\end{equation}\n",
    "\n",
    "As can be concluded from the limit case above, the Laplace transform converges only for $\\Re \\{ s + s_0 \\} > 0$. Hence, the ROC is given as\n",
    "\n",
    "\\begin{equation}\n",
    "\\Re \\{ s \\} > \\Re \\{ - s_0 \\} \n",
    "\\end{equation}\n",
    "\n",
    "Combining above findings, the transformation of the causal complex exponential signal reads\n",
    "\n",
    "\\begin{equation}\n",
    "\\mathcal{L} \\{ \\epsilon(t) \\cdot e^{-s_0 t} \\} = \\frac{1}{s + s_0} \\qquad \\text{for } \\Re \\{ s \\} > \\Re \\{ - s_0 \\}\n",
    "\\end{equation}"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Example - Transformation of exponential signal**\n",
    "\n",
    "In `SymPy` the [Laplace transform](http://docs.sympy.org/latest/modules/integrals/integrals.html?highlight=laplace#sympy.integrals.transforms.laplace_transform) is defined as one-sided transformation. The respective function of `SymPy` is utilized in the following to calculate the transform of the causal complex exponential signal."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
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      "text/latex": [
       "$$\\left ( \\frac{1}{s + s_{0}}, \\quad 0, \\quad \\left|{\\arg{\\left (s_{0} \\right )}}\\right| < \\frac{\\pi}{2}\\right )$$"
      ],
      "text/plain": [
       "⎛  1                    π⎞\n",
       "⎜──────, 0, │arg(s₀)│ < ─⎟\n",
       "⎝s + s₀                 2⎠"
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "s0 = sym.symbols('s0', complex=True)\n",
    "\n",
    "X, a, cond = sym.laplace_transform(sym.exp(-s0*t), t, s)\n",
    "X, a, cond"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The function returns three results. The first result is the Laplace transform $X(s)$, the second result $a$ is the half-plane of convergence with $\\Re \\{ s \\} > a$ and the third result represents an auxiliary convergence condition."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Transformation of the Heaviside Signal\n",
    "\n",
    "The Laplace transform of the [Heaviside signal](../continuous_signals/standard_signals.ipynb#Heaviside-Signal) is derived from above transform of the causal complex exponential signal $\\epsilon(t) \\cdot e^{-s_0 t}$ by setting $s_0 = 0$\n",
    "\n",
    "\\begin{equation}\n",
    "\\mathcal{L} \\{ \\epsilon(t) \\} = \\frac{1}{s} \\qquad \\text{for } \\Re \\{ s \\} > 0\n",
    "\\end{equation}"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Convergence\n",
    "\n",
    "A sufficient but not necessary condition for the existence of the Laplace transform $X(s) = \\mathcal{L} \\{ x(t) \\}$ of a given signal $x(t)$ is\n",
    "\n",
    "\\begin{equation}\n",
    "\\int_{-\\infty}^{\\infty} | x(t) \\cdot e^{- \\sigma t} | \\; dt < \\infty\n",
    "\\end{equation}\n",
    "\n",
    "where $\\sigma = \\Re\\{ s \\}$ denotes the real part of the complex frequency $s = \\sigma + j \\omega$ of the Laplace transform. Formally the signal $x(t)$ has to be a [locally integrable function](https://en.wikipedia.org/wiki/Locally_integrable_function).\n",
    "\n",
    "The imaginary part $\\omega = \\Im \\{ s \\}$ of the complex frequency $s$ has no effect in terms of convergence. Consequently, the ROC is determined solely by its real part $\\sigma = \\Re\\{ s \\}$. For a right-sided signal with $x(t) = 0$ for $t < T_0$, the ROC is given in the form of $\\Re \\{ s \\} > a$ with $a \\in \\mathbb{R}$. This can be concluded from the decay of the exponential term $e^{- \\sigma t}$ for $t \\to \\infty$, which ensures convergence for a given $a$. However this reasoning holds only for signals with [exponential growth](https://en.wikipedia.org/wiki/Exponential_growth). Please refer to the [Laplace transform of the causal exponential signal](#Transformation-of-the-Causal-Complex-Exponential-Signal) for an example. \n",
    "\n",
    "The same reasoning leads to the ROCs for a left-sided and two-sided signal. The resulting ROCs are shown in the following illustration\n",
    "\n",
    "![Region of convergence for left-/two-/right-sided signal](ROC.png)\n",
    "\n",
    "The gray areas denote the values $s$ for which the Laplace transformation converges. The borders $a$ of these areas (dashed lines) depend on the signal $x(t)$. A more detailed discussion of the ROCs for the Laplace transform can be found in the literature, e.g. [[Girod et al.](index.ipynb#Literature)]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Representation\n",
    "\n",
    "The Laplace transform $X(s) = \\mathcal{L} \\{ x(t) \\}$ depends on the complex frequency $s \\in \\mathbb{C}$ and is in general complex valued $X(s) \\in \\mathbb{C}$. It can be illustrated by plotting its magnitude $|X(s)|$ and phase $\\varphi (s)$ or real $\\Re \\{ X(s) \\}$ and imaginary $\\Im \\{ X(s) \\}$ part in the complex $s$-plane. The resulting three-dimensional plots are often not very illustrative. \n",
    "\n",
    "However, many Laplace transforms of interest in the theory of signals and systems are [rational functions](https://en.wikipedia.org/wiki/Rational_function) in $s$. The polynomials of the numerator and denominator can be represented by their complex [roots](https://en.wikipedia.org/wiki/Zero_of_a_function#Polynomial_roots) and a constant factor. The roots of the numerator are termed as *zeros* while the roots of the denominator are termed as *poles* of $X(s)$. The polynomial and the zero/pole representation of a rational Laplace transform are equivalent\n",
    "\n",
    "\\begin{equation}\n",
    "X(s) = \\frac{\\sum_{m=0}^{M} \\beta_m s^m}{\\sum_{n=0}^{N} \\alpha_n s^n} = K \\cdot \\frac{\\prod_{\\mu=0}^{Q} (s - s_{0 \\mu})}{\\prod_{\\nu=0}^{P} (s - s_{\\infty \\nu})}\n",
    "\\end{equation}\n",
    "\n",
    "where $M$ and $N$ denote the order of the numerator/denominator polynomial, $s_{0 \\mu}$ and $s_{\\infty \\nu}$ the $\\mu$-th zero/$\\nu$-th pole of $X(s)$, and $Q = M-1$ and $P = N-1$ the total number of zeros and poles, respectively. For $M=N$ the factor $K = \\frac{\\beta_M}{\\alpha_N}$. If $M > N$ at least one pole is located at $|s| = \\infty$.\n",
    "\n",
    "It is common to illustrate the poles and zeros in a [pole-zero plot](https://en.wikipedia.org/wiki/Pole%E2%80%93zero_plot). Here the locations of the complex poles and zeros, their degrees and the factor $K$ are plotted in the $s$-plane\n",
    "\n",
    "![Illustration of the pole and zero locations in a pole-zero plot](pz_plot.png)\n",
    "\n",
    "The locations of the poles and zeros provide insights into the composition of a signal. For instance, the Laplace transform of the [complex exponential signal](#Transformation-of-the-Causal-Complex-Exponential-Signal) has a pole at $s = - s_0$. A signal which is composed from a superposition of complex exponential signals will have multiple poles whose positions are related to the complex frequencies it is composed of."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Exercise**\n",
    "\n",
    "* Derive $X(s)$ together with its ROC from above pole-zero plot."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Example - Illustration of Laplace transform of the exponential signal**\n",
    "\n",
    "The Laplace transform of the causal complex exponential function\n",
    "\n",
    "\\begin{equation}\n",
    "X(s) = \\frac{1}{s + s_0} \\qquad \\text{for } \\Re \\{ s \\} > \\Re \\{ - s_0 \\}\n",
    "\\end{equation}\n",
    "\n",
    "is illustrated by plotting its magnitude $|X(s)|$ in the $s$-plane $s = \\sigma + j \\omega$ for $s_0 = 1 + j$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
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    {
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   ],
   "source": [
    "sigma, omega = sym.symbols('sigma omega')\n",
    "\n",
    "X = 1/(s + s0)\n",
    "X1 = X.subs({s: sigma+sym.I*omega, s0: 1+sym.I})\n",
    "\n",
    "sym.plotting.plot3d(abs(X1), (sigma, -2, 2), (omega, -2, 2),\n",
    "                    xlabel=r'$\\Re\\{s\\}$', ylabel=r'$\\Im\\{s\\}$', title=r'$|X(s)|$');"
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  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Alternatively, the Laplace transform is illustrated by its pole-zero plot. First the poles"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
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      "text/latex": [
       "$$\\left \\{ - s_{0} : 1\\right \\}$$"
      ],
      "text/plain": [
       "{-s₀: 1}"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "poles = sym.roots(sym.denom(X), s)\n",
    "poles"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "and zeros are computed"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAABMAAAAVBAMAAABWJ8jiAAAAMFBMVEX///8AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAv3aB7AAAAD3RSTlMAEER2zVSJ3ZkiZjKru+/kt61jAAAACXBIWXMAAA7EAAAOxAGVKw4bAAAAaklEQVQIHWNgYGBUYuCMZAADk0AGhj0XQUzWjyDyDohgKwCR6aQyORxAOuxAxPwFYDIAaHgRiMXAeSWAgbFFAMRkcwISvAdAzPgJQAJiWx6IT4rFzA9AOlpABONTEPEKxGSYcZSBOwdoLwBIYxoX0L7jfAAAAABJRU5ErkJggg==\n",
      "text/latex": [
       "$$\\left \\{ \\right \\}$$"
      ],
      "text/plain": [
       "{}"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "zeros = sym.roots(sym.numer(X), s)\n",
    "zeros"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Above dictionaries are composed of the poles and zeros, and their degrees. \n",
    "\n",
    "In order to illustrate the location of poles and zeros in the $s$-plane, a function is defined for a pole-zero plot using the Python library [`matplotlib`](http://matplotlib.org/)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "\n",
    "def pole_zero_plot(poles, zeros, ax=None):\n",
    "    \n",
    "    for pole in poles:\n",
    "        plt.plot(complex(pole).real, complex(pole).imag, 'rx', markersize=10)\n",
    "    for zero in zeros:\n",
    "        plt.plot(complex(zero).real, complex(zero).imag, 'bo', markersize=10)\n",
    "    \n",
    "    if ax is None:\n",
    "        ax = plt.gca()\n",
    "    ax.set_aspect(1)\n",
    "    \n",
    "    plt.axis([-2, 2, -2, 2])\n",
    "    plt.xlabel(r'$\\Re \\{ s \\}$')\n",
    "    plt.ylabel(r'$\\Im \\{ s \\}$')\n",
    "    plt.grid()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The pole-zero plot is shown for $s_0 = 1 + j$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
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   "source": [
    "X2 = X.subs(s0, 1+sym.I)\n",
    "pole_zero_plot(sym.roots(sym.denom(X2), s), sym.roots(sym.numer(X2), s))"
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    "**Copyright**\n",
    "\n",
    "This notebook is provided as [Open Educational Resource](https://en.wikipedia.org/wiki/Open_educational_resources). Feel free to use the notebook for your own purposes. The text is licensed under [Creative Commons Attribution 4.0](https://creativecommons.org/licenses/by/4.0/), the code of the IPython examples under the [MIT license](https://opensource.org/licenses/MIT). Please attribute the work as follows: *Sascha Spors, Continuous- and Discrete-Time Signals and Systems - Theory and Computational Examples*."
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